Glentoran have urged the Irish Football Association to further increase the capacity at the Oval for their 2 May cup final against Portadown.
Temporary seating is to be installed for the big domestic showpiece but the Glens say their 2,000 additional tickets sold out in just 85 minutes.
The capacity had been increased to 8,200 for the match against Portadown.
The game is being played at Glentoran's ground as Windsor Park is closed after structural faults were discovered.
Cracks were found in Windsor's west stand which is now to be demolished.
Glentoran claim the company installing the extra seating at the Sydenham end of the Oval had indicated that more could be erected.
The east Belfast club's chairman Stephen Henderson said unlucky fans had been turned away on Wednesday and that they could have sold another 1,500 tickets.
Meanwhile, Portadown have been given assurances over the safety of their supporters.
Ports assistant manager Kieran Harding said on Tuesday that it was "well documented that the club's supporters don't feel particularly confident going to the Oval" following a number of previous incidents.
However, Harding said the Shamrock Park club had held discussions with the Irish FA over the issue.
"At the minute, they have satisfied us that they will take all the necessary precautions that our supporters will be protected and we have got to take them at their word," added the Portadown assistant manager.